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17704Re: primes of the form q^2-q+1...

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  • Werner D. Sand
    Feb 28, 2006
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      Hello Max,

      Some simple partial results:

      Let q=2^p-1; a=q²-q+1 then
      q=0 mod 3, if p is even
      q=1 mod 3, if p is odd (e.g. prime)
      in any case a=1 mod 3
      a is not divisible by 2,3,5; the more amazing that a=prime does not
      occur (p>3).
      a cannot be factorized within the real numbers such as e.g.
      a²-b²=(a+b)*(a-b).

      Werner
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